Toy building blocks are known each of parallelepipedal shape and having an upper surface formed with a plurality of bosses. The lower surface of each of the blocks is formed with a plurality of concavities or sockets each adapted to receive a respective boss. Usually the block simply has an apron that engages around the bosses of the underlying blocks. The principal disadvantage of these systems is that they are relatively difficult for a child to line up in order to snap them together. Furthermore after much use they frequently wear and deform slightly so that a construction formed with such blocks comes readily apart. Another disadvantage is that it is difficult with such blocks to snap them together in any other than two different manners: either one directly on top of the other, or one half on top of the other.